Publication de 6 numéros par an
ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352
Indexed in
ADAPTIVE WAVELET ALGORITHM FOR SOLVING NONLINEAR INITIAL–BOUNDARY VALUE PROBLEMS WITH ERROR CONTROL
RÉSUMÉ
We present a numerical method which exploits the biorthogonal interpolating wavelet family, and second-generation wavelets, to solve initial–boundary value problems on finite domains. Our predictor-corrector algorithm constructs a dynamically adaptive computational grid with significant data compression, and provides explicit error control. Error estimates are provided for the wavelet representation of functions, their derivatives, and the nonlinear product of functions. The method is verified on traditional nonlinear problems such as Burgers' equation and the Sod shock tube. Numerical analysis shows polynomial convergence with negligible global energy dissipation.
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van Tuijl Rody A., Harnish Cale, Matouš Karel, Remmers Joris J. C., Geers Marc G. D., Wavelet based reduced order models for microstructural analyses, Computational Mechanics, 63, 3, 2019. Crossref
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van Tuijl Rody A., Remmers Joris J.C., Geers Marc G.D., Multi-dimensional wavelet reduction for the homogenisation of microstructures, Computer Methods in Applied Mechanics and Engineering, 359, 2020. Crossref
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Kaiser Tobias, Remmers Joris J. C., Geers Marc G. D., An adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanics, Computational Mechanics, 2022. Crossref